相关论文: Invariant Set Estimation for Piecewise Affine Dyna…

Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers…

In this paper we address a practical aspect of differential barrier penalty functions in linear programming. In this respect we propose an affine scaling interior point algorithm based on a large classe of differential barrier functions.…

Deep neural networks, particularly those employing Rectified Linear Units (ReLU), are often perceived as complex, high-dimensional, non-linear systems. This complexity poses a significant challenge to understanding their internal learning…

The large number of ReLU non-linearity operations in existing deep neural networks makes them ill-suited for latency-efficient private inference (PI). Existing techniques to reduce ReLU operations often involve manual effort and sacrifice…

We present a real-time multivariate anomaly detection algorithm for data streams based on the Probabilistic Exponentially Weighted Moving Average (PEWMA). Our formulation is resilient to (abrupt transient, abrupt distributional, and gradual…

In this report, we analyze and design feedback policies for discrete-time Piecewise-Affine (PWA) systems with uncertainty in both the affine dynamics and the polytopic partition. The main idea is to utilise the Difference-of-Convex (DC)…

Verification of neural networks relies on activation functions being piecewise affine (pwa) -- enabling an encoding of the verification problem for theorem provers. In this paper, we present the first formalization of pwa activation…

This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…

We propose ReDense as a simple and low complexity way to improve the performance of trained neural networks. We use a combination of random weights and rectified linear unit (ReLU) activation function to add a ReLU dense (ReDense) layer to…

Today, it is more important than ever before for users to have trust in the models they use. As Machine Learning models fall under increased regulatory scrutiny and begin to see more applications in high-stakes situations, it becomes…

In this paper, we consider the problem of automatically designing a Rectified Linear Unit (ReLU) Neural Network (NN) architecture (number of layers and number of neurons per layer) with the guarantee that it is sufficiently parametrized to…

Piecewise linearization is a key technique for solving nonlinear problems in transportation network design and other optimization fields, in which generating breakpoints is a fundamental task. This paper proposes an optimal breakpoint…

We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…

In this work, the issue of estimation of reachable sets in continuous bimodal piecewise affine systems is studied. A new method is proposed, in the framework of ellipsoidal bounding, using piecewise quadratic Lyapunov functions. Although…

Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address…

This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…

Obtaining control barrier functions (CBFs) with large safe sets for complex nonlinear systems and constraints is a challenging task. Predictive CBFs address this issue by using an online finite-horizon optimal control problem that…

We give the first dimension-efficient algorithms for learning Rectified Linear Units (ReLUs), which are functions of the form $\mathbf{x} \mapsto \max(0, \mathbf{w} \cdot \mathbf{x})$ with $\mathbf{w} \in \mathbb{S}^{n-1}$. Our algorithm…

We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…

We study stochastic systems characterized by difference inclusions. Such stochastic differential inclusions are defined by set-valued maps involving the current state and stochastic input. For such systems, we investigate the problem of…